Conventionally people attribute the execution of Anne to her "failure" to produce a male heir. However, this can't have been the actual reason she fell from grace, right? I mean she was still young enough to conceive, and they had not been married all that long.
I think the place to start is: we can never really know. I don't bother to say this for most answers on this sub (since it's self-evident), but the field of pop Tudor history is so glutted with authors presenting definitive motives for various events in order to stand out from each other that I think it's worthwhile to note here. So much of what we know about this period comes from legal documents and the correspondence of ambassadors, not private diaries; the Spanish ambassadors are particularly tricky sources, because they were often wildly partisan due to Catherine of Aragon's relationship to the Hapsburg emperor. This is why people can write Anne Boleyn as a virtuous innocent or as a scheming harpy without either one being considered alternate history - there is so much room for interpretation.
I want to start out with a few paragraphs c/p'd from a past answer of mine to provide some context for Henry and Anne's marriage:
Henry believed that if he were with the right woman and God blessed their union, a son would be granted to them. Remember that a major factor in his stated reasoning for divorcing Catherine of Aragon was that he claimed to believe she and his brother had consummated their marriage, and that therefore he had sinned by marrying her and was being punished with daughters, stillbirths, and children who died young. If he corrected his error, then God would be like, "Now we're good!" and provide a healthy, male heir to the throne.
When Henry met Anne, she was about 25 (and he was about 35), and he was highly attracted to her. She initially rejected his advances on the grounds that good girls don't get involved in extramarital/premarital relationships, which led to his desire to make her his mistress morphing into a desire to make her his wife, and despite the fact that it took seven years, he followed through. Catherine's track record of unsuccessful pregnancies and apparent menopause were a large factor in his interest in a younger bride, but by all accounts Henry was in love with Anne. His feelings were strong enough to keep the unconsummated relationship going for years and to result in a massive break from the Catholic Church and from an alliance with Spain and the Holy Roman Empire. And at the same time, 32 is not old for childbearing - certainly it would have been an unusual age for a first birth, but women typically gave birth into their thirties. Given that Anne became pregnant pretty much right away after the marriage, it seemed reasonable to believe that the problem was fixed.
However, of course, Anne did not have any sons. This fed back into the question of whether she were the right woman and whether God approved of this marriage (which only happened because he broke with the pope and ended his previous marriage before the death of his wife, two things historically seen as against God's wishes). Sure, Anne theoretically had time to produce more sons, but if God wanted to show that Henry had made the right choices, wouldn't He have sent them immediately? It's certainly not the be-all-end-all, but in the kind of atmosphere created by the English Reformation, this was certainly cause for anxiety.
Then I'm going to quote from another answer of mine:
Anne was accused of having slept with her own brother, George, Viscount of Rochford, as well as Sir William Brereton, Sir Francis Weston, Sir Henry Norris, and Mark Smeaton; Brereton, Weston, and Norris were all members of Henry's privy chamber (his inner circle), and Smeaton was a musician at court. Even worse, she was accused of having conspired at Henry's death in order to marry one of them. The times and places of the alleged adulterous incidents didn't really work out - she was accused of sleeping with Norris a month after she gave birth to Elizabeth, for instance, and of sleeping with Brereton at Hampton Court Palace a few months later when the whole court was at Greenwich - but that didn't matter. Men of the period were horrified and terrified of the specter of the adulterous wife, who debased their right to have sex with her by sharing it with others, and who put the paternity of all her children in doubt. Perhaps even worse, she put them into the ridiculed position of the cuckold, a man who couldn't control his wife. it was far more important to the all-male court to denounce the adultery and make it clear to other women (and the men who might sleep with them) that they would face high penalties for it. Henry was feeling all of this and the jury knew what he wanted them to do.
...
Eric Ives argues that much of the machinery of the trial for adultery was put into motion by Thomas Cromwell (Henry's highly influential officer) without Henry's knowledge, as a way to force Anne's fall from grace. Cromwell and Anne were very opposed in politics, and it would have been to Cromwell's benefit to remove her ability to influence Henry and public opinion. The Spanish ambassador, Eustace Chapuys, claimed that Cromwell told him Anne was out of favor even as Henry was insisting on her being recognized by foreign courts as the rightful queen. Cromwell then told Henry that she was an adulteress, probably capitalizing on her miscarriage just a few months earlier of a fetus said to be male, and tortured Mark Smeaton into a confession, and then Anne was very suddenly arrested. (After her arrest, she was unwittingly pumped for incriminating information that was then inflated and used to create compelling specific charges.) Under this theory, Henry simply wasn't that interested in getting a new queen before that point. He was beginning to pay attention to Jane Seymour, but there was no indication that it was serious enough to result in another rupture and a new queen until he turned from Anne - Ives describes his attentions as "courtly" practically all the way up to Anne's trial.
Once Anne was accused of adultery, that was it.